Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary ‎condition‎

الموضوعات : مجله بین المللی ریاضیات صنعتی

J. Biazar ¹ (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.)
T. Houlari ² (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.)

تاريخ الإرسال : 18 الخميس , ذو الحجة, 1436 تاريخ التأكيد : 18 الخميس , ذو الحجة, 1436 تاريخ الإصدار : 18 الخميس , ذو الحجة, 1436

الکلمات المفتاحية: Ill-posed inverse problems, Sinc-Galerkin method, Tikhonov regularization, ‎U‎nkown boundary ‎condition,

ملخص المقالة :

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $x=a'$, and determining $u(a',t)$ a stable solution will be achived. An illustrative example is provided to show the ability and the efficiency of this numerical ‎approach.‎